Commit df26c800 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 4c823baa
Pipeline #13707 canceled with stage
......@@ -69,13 +69,15 @@ PRINCIPALES COMBINAISONS
<summary>Expressions en coordonnées cylindriques et sphériques</summary>
* coordonnées cylindriques $`(\rho\,,\,\varphi\,,\,z)`$ :
<br>
$`\Delta\,\phi=\dfrac{1}{\rho}\dfrac{\partial}{\partial \rho}\left(\rho\,\dfrac{\partial \phi}{\partial \rho}\right)
+\dfrac{1}{\rho^2}\dfrac{\partial^2 \phi}{\partial \varphi^2}+\dfrac{\partial^2 \phi}{\partial z^2}`$
$`\Delta\,\phi=\dfrac{1}{\rho}\cdot\dfrac{\partial}{\partial \rho}\left(\rho\,\dfrac{\partial \phi}{\partial \rho}\right)`$
$`+\dfrac{1}{\rho^2}\cdot\dfrac{\partial^2 \phi}{\partial \varphi^2}`$
$`+\dfrac{\partial^2 \phi}{\partial z^2}`$
<br>
* coordonnées sphérique $`(r\,,\,\theta\,,\,\varphi)`$ :
<br>
$`\Delta\,\phi=\dfrac{1}{r}\dfrac{\partial^2}{\partial r^2}(r\phi)+
\dfrac{1}{r^2\,\sin\theta}\dfrac{\partial}{\partial \theta}\left(\sin\theta\dfrac{\partial \phi}{\partial \theta}\right)+
\dfrac{1}{r^2\,\sin^2\theta}\dfrac{\partial^2 \phi}{\partial \varphi^2}`$
$`\Delta\,\phi=\dfrac{1}{r}\cdot\dfrac{\partial^2}{\partial r^2}(r\phi)`$
$`+\dfrac{1}{r^2\,\sin\theta}\cdot\dfrac{\partial}{\partial \theta}\left(\sin\theta\dfrac{\partial \phi}{\partial \theta}\right)`$
$`+\dfrac{1}{r^2\,\sin^2\theta}\cdot\dfrac{\partial^2 \phi}{\partial \varphi^2}`$
---
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